THE CANTERBURY PUZZLES
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we go the same distance, for every one of the eight straight portions
of this path measures exactly 25 yards. Similarly in Fig. 2,
the zig-zag contains ten straight portions each 20 yards long : that
path is also the same length—200 yards. No matter how many
steps we make in our zig-zag path, the result is most certainly
always the same. Thus, in Fig. 3 the steps are very small, yet the
distance must be 200 yards, as is also the case in Fig. 4, and
would yet be if we needed a microscope to detect the steps.
In this way, the Friar
argued, we may go on
straightening out that
zig-zag path until we
ultimately reach a per-
fectly straight line, and
it therefore follows that
the diagonal of a square
is of exactly the same
length as two of the
sides.
Now, in the face of
it, this must be wrong :
and it is in fact absurdly
so, as we can at once
3
4?
prove by actual mea-
surement if we have any doubt. Yet the Sompnour could not for
the life of him point out the fallacy and so upset the Friar's reasoning.
It was this that so exasperated him and consequently, like many
of us to-day when we get entangled in an argument, he utterly
lost his temper and resorted to abuse. In fact, if some of the
other pilgrims had not interposed the two would have undoubtedly
come to blows. The reader will perhaps at once see the flaw in the
Friar's argument.
29.—
Chaucer's Puzzle.
Chaucer himself accompanied the pilgrims. Being a mathema-
tician and a man of a thoughtful habit, the Host made
fun
of him,
28
